An elephant walks east for a distance of 58 km, then walks north for a distance of 16 km and finally north east at 300 for 15 km. Find the magnitude of the elephant’s total displacement in kilometers.
now would i find the change in distance by subtracting numbers and the using the |v|= sqrt (x^2) + (y^2) to find the magnitude
D = 58 + 16[90o] + 15[45o].
X = 58 + 16*Cos90 + 15*Cos45 =
58 + 0 + 10.6 = 68.4 km.
Y = 0 + 16*sin90 + 15*sin45 =
0 + 16 10.6 = 26.6 km.
D = sqrt(X^2 + Y^2) km.
Note: Northeast = 45o N. of E.
To find the magnitude of the elephant’s total displacement, you can follow these steps:
1. Start by calculating the eastward displacement. Since the elephant walks east for 58 km and there is no northward component, the eastward displacement is 58 km.
2. Next, determine the northward displacement. The elephant walks north for 16 km, so the northward displacement is 16 km.
3. Now, let's calculate the northeast displacement. To do this, we need to break down the displacement into its eastward and northward components. Since the direction is northeast at an angle of 300° and the displacement is 15 km, we can use trigonometry to find the components.
- The eastward component = 15 km * cos(300°)
- The northward component = 15 km * sin(300°)
4. Add up all the eastward components: 58 km (from step 1) + eastward component (from northeast displacement).
5. Add up all the northward components: 16 km (from step 2) + northward component (from northeast displacement).
6. Now you have the total eastward displacement and the total northward displacement. To find the magnitude (total displacement), use the formula:
|v| = sqrt(x^2 + y^2)
Where x is the total eastward displacement and y is the total northward displacement.
By substituting the values into the formula, you can find the magnitude of the elephant’s total displacement in kilometers.